Note: Try this answer if you continue to face the issue even after attempting the steps in @ramsudharsan's answer. If you have not tried following those instructions yet I recommend you to do so since that seems to fix the problem in most cases.
It seems that you have a bad superblock. To fix this:
Firstly, boot into a live CD or USB
Find out your partition number by using
sudo fdisk -l|grep Linux|grep -Ev 'swap'
Then, list all superblocks by using the command:
sudo dumpe2fs /dev/sda2 | grep superblock
sda2 to your drive number
You should get a similar output like this
Primary superblock at 0, Group descriptors at 1-6
Backup superblock at 32768, Group descriptors at 32769-32774
Backup superblock at 98304, Group descriptors at 98305-98310
Backup superblock at 163840, Group descriptors at 163841-163846
Backup superblock at 229376, Group descriptors at 229377-229382
Backup superblock at 294912, Group descriptors at 294913-294918
Backup superblock at 819200, Group descriptors at 819201-819206
Backup superblock at 884736, Group descriptors at 884737-884742
Backup superblock at 1605632, Group descriptors at 1605633-1605638
Backup superblock at 2654208, Group descriptors at 2654209-2654214
Backup superblock at 4096000, Group descriptors at 4096001-4096006
Backup superblock at 7962624, Group descriptors at 7962625-7962630
Backup superblock at 11239424, Group descriptors at 11239425-11239430
Backup superblock at 20480000, Group descriptors at 20480001-20480006
Backup superblock at 23887872, Group descriptors at 23887873-23887878
Choose an alternate superblock from this list, for this case alternate superblock # 32768
Now, to check and repair a Linux file system using alternate superblock # 32768:
sudo fsck -b 32768 /dev/sda2 -y
-y flag is used to skip all the
Fix? questions and to answer them all with a yes automatically
You should get similar output like this:
fsck 1.40.2 (12-Jul-2007)
e2fsck 1.40.2 (12-Jul-2007)
/dev/sda2 was not cleanly unmounted, check forced.
Pass 1: Checking inodes, blocks, and sizes
Pass 2: Checking directory structure
Pass 3: Checking directory connectivity
Pass 4: Checking reference counts
Pass 5: Checking group summary information
Free blocks count wrong for group #241 (32254, counted=32253).
Free blocks count wrong for group #362 (32254, counted=32248).
Free blocks count wrong for group #368 (32254, counted=27774).
/dev/sda2: ***** FILE SYSTEM WAS MODIFIED *****
/dev/sda2: 59586/30539776 files (0.6% non-contiguous), 3604682/61059048 blocks
Now try mounting the partition
sudo mount /dev/sda2 /mnt
Now, try to browse the filesystem with the following commands
cp file /path/to/safe/location
If you are able to perform the above commands, you have most probably fixed your error.
Now, restart you computer and you should be able to boot normally.